Related for Rosh Hashanah 13:3
ת"ר באחד בניסן ראש השנה לחדשים ולעיבורין ולתרומת שקלים וי"א אף לשכירות בתים
for leap-years,<span class="x" onmousemove="('comment',' V. infra.');"><sup>5</sup></span> and for the offering of shekalim;<span class="x" onmousemove="('comment',' For first using for the purchase of congregational sacrifices the shekalim that were collected in Adar. Cf. Meg. 29b.');"><sup>6</sup></span>
Tosefta Rosh Hashanah (Lieberman)
[The month] Nisan is the beginning of the year for the kings, pilgrimage festivals, months, and the collection of the temple tax. Some say: Also for renting houses. How [one should understand]: "for the kings"? [Answer:] If he dies in Adar and another takes his place in Adar, the year is counted both for him and for the other. If he dies in Nisan and another takes his place in Nisan, the year is counted both for him and for the other. If [one] dies in Adar and another takes his place in Nisan, the first [year] is counted for the first and the second [year] for the second.
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